Question 1

What does the y⁺ calculator compute?

Accepted Answer

The calculator determines the required first cell height Δy for a target y⁺ value. The procedure is: (1) estimate skin friction coefficient Cf ≈ 0.058×Re⁻⁰·² (turbulent flat plate), (2) compute wall shear stress τ_w = Cf×ρU²/2, (3) compute friction velocity u_τ = √(τ_w/ρ), (4) compute first cell height Δy = y⁺ × ν / u_τ. For air at Re = 10⁶ with target y⁺ = 1, a typical result is Δy ≈ 1–5 μm.

Question 2

How do I use the y⁺ calculator?

Accepted Answer

1. Set Reynolds number (10⁴–10⁸) using the log-scale slider. 2. Enter the characteristic length L (0.01–100 m). 3. Select the fluid (water, air, or custom ρ and μ). 4. Set the target y⁺ (0.1–300). 5. Select the turbulence model (k-ε, k-ω SST, Spalart-Allmaras, or LES) to see its recommended y⁺ range and mesh guidance. Use the resulting Δy as the first-layer height in your CFD mesh generator.

Question 3

What is y⁺ (y-plus) and why is it critical in CFD meshing?

Accepted Answer

y⁺ is the dimensionless wall distance defined as y⁺ = u_τ × Δy / ν. It locates the first mesh cell within the boundary layer structure: the viscous sublayer (y⁺ < 5), the buffer layer (5 < y⁺ < 30), and the log-law region (y⁺ > 30). Correct y⁺ placement is essential for accurate predictions of wall shear stress, heat transfer, and flow separation. Using the wrong y⁺ for a given turbulence model can introduce errors of 10–30% in friction and heat transfer results.

Question 4

What y⁺ value should I target for k-ω SST vs k-ε standard?

Accepted Answer

k-ω SST uses Low-Re (near-wall) treatment and requires y⁺ < 1 (ideally y⁺ ≈ 0.5–1) to directly resolve the viscous sublayer. This gives accurate results for flows with adverse pressure gradients, separation, and reattachment. k-ε standard uses wall functions based on the log law and requires y⁺ = 30–100, placing the first cell in the fully turbulent log-law region. Using k-ε with y⁺ < 11 degrades accuracy because the wall function is applied outside its valid range. Spalart-Allmaras supports both modes; LES mandates y⁺ < 1 at the wall.

CFD Near-Wall y⁺ Calculator Mesh Tool

Flow Conditions

Required First Cell Thickness Δy vs Reynolds Number (log-log)